THE EXACT NUMERICAL-SOLUTION OF A SCHRODINGER-EQUATION WITH 2-COULOMB CENTERS PLUS OSCILLATOR POTENTIAL

A numerical technique of solving the Schrodinger equation with two-Coulomb centres plus the oscillator Hamiltonian has been developed. A scheme of evaluating energy levels and wavefunctions of such a Hamiltonian is described in some detail. The proposed algorithm also allows the study of analytical properties of energy levels in a complex plane of the internuclear distance, i.e. to find positions of branch points in the complex plane. The prolate ellipsoidal coordinates enable separation of variables in the equation studied which greatly facilitates the solution. A numerical method for finding branch point positions for an arbitrary analytical function is outlined.